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Zbl 1217.34009
Caballero, J.; Harjani, J.; Sadarangani, K.
Existence and uniqueness of positive solution for a boundary value problem of fractional order. (English)
[J] Abstr. Appl. Anal. 2011, Article ID 165641, 12 p. (2011). ISSN 1085-3375; ISSN 1687-0409/e

Summary: We are concerned with the existence and uniqueness of positive solutions for the following nonlinear fractional boundary value problem: $D^{\alpha}_{0+}u(t) + f(t, u(t)) = 0, 0 \leq t \leq 1, 3 < \alpha \leq 4$, $u(0) = u'(0) = u''(0) = u''(1) = 0$, where $D^{\alpha}_{0+}$ denotes the standard Riemann-Liouville fractional derivative. Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also given to illustrate the results.

MSC 2000:: *34A08

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Zentralblatt MATH Berlin [Germany]